求解双相和黏弹性介质波传播方程的间断有限元方法及其波场模拟

间断有限元（Discontinuous Galerkin：DG）方法具有低数值频散、网格剖分灵活、能模拟地震波在复杂介质中传播等优点.因此,本文将一种新的DG方法推广到双相和黏弹性等复杂介质的地震波场模拟,发展了求解Biot弹性波方程和D'Alembert介质波动方程的DG方法.首先通过引入辅助变量将Biot双相介质弹性波方程和D'Alembert介质波动方程转化为关于时间-空间的一阶偏微分方程组,然后对该方程组进行DG空间离散,得到半离散化的常微分方程组.最后,对此常微分方程组,应用加权的Runge-Kutta格式进行时间推进计算.数值结果表明,DG方法可以有效地求解Biot双相介质弹性波方程和D'Alembert介质波动方程,并能很好地压制因离散求解波动方程而产生的数值频散,获得清晰的各种地震波震相.     

起伏地表下地震波传播数值模拟方法研究进展

起伏地表是地震数据的采集、处理和解释中普遍遇到的难题.起伏地表下的地震波传播数值模拟,对起伏地表观测的地震资料处理解释有重要意义.地震波场模拟和地震波走时场分别描述地震波的动力学和运动学信息,为研究地震波传播理论的两种重要途径.本文从地震波场和地震波走时场两方面回顾和总结了起伏地表下的地震波传播数值模拟方法的研究进展,并展示了该领域的一些最新研究成果,为使读者能从中找到突破点,为起伏地表这一勘探领域的经典难题做出贡献.     

地震波有限差分模拟综述

本文从有限差分法数值模拟技术的各个方面对地震波有限差分模拟的发展和现状进行了论述.波场的数值模拟技术是认识地震波传播规律,检验各种处理方法正确性的重要工具,地震波的数值模拟是地震波传播规律研究的必要手段,贯穿于地震资料的采集、处理、解释的整个过程中.有限差分法数值模拟技术相对于射线方法具有更高的精度,同时比有限元方法计算量小,因此在实际应用中占很重要的地位.     

复杂固-液介质的速度应力方程三角形单元间断伽辽金地震波模拟算法

间断伽辽金法可用于存在复杂边界条件的模型,同时具有高阶精度和易于并行计算的优点,因此近年来在地震波传播模拟研究中得到了快速发展.数值通量是间断伽辽金法的关键组成部分之一.相比于其他通量,基于Rankine-Hugoniot跳跃条件的通量(RH-condition通量)在固体和液体介质边界具有更宽的稳定性,可以使用更大的时间步长,尤其是液体和固体之间的波阻抗差异较大时.它已被用于基于四边形网格和速度-应变方程的间断伽辽金地震波固液介质模拟.本文为了模拟陆地自然水体等存在复杂固-液界面形状的地震波传播,并在未来与其他数值方法耦合,发展了基于三角形网格的RH-condition通量间断伽辽金方法,使用一阶速度-压力声波和一阶速度-应力弹性波方程模拟复杂固-液介质中地震波的传播.通过水平层状和sin型起伏固-液模型,验证了该方法模拟结果的准确性.通过数值模拟展示了所提出的间断伽辽金法在不同网格大小和阶数下的准确性和效率.最后通过一个复杂模型的例子表明存在复杂固-液界面时该方法可以准确施加固-液边界条件.     

基于非结构网格求解三维D'Alembert介质中声波方程的并行加权Runge-Kutta间断有限元方法

间断有限元方法(Discontinuous Galerkin method,简称DGM)在求解地震波动方程时具有低数值频散、网格剖分灵活等优点,因此,为适应数值模拟对模拟精度和复杂地质结构的要求,本文提出一种新的加权Runge-Kutta间断有限元(weighted Runge-Kutta discontinuous ...     

各向同性介质中射线理论与有限差分地震波场模拟方法比较研究

地震波场数值模拟不仅是研究复杂地区地震资料采集、处理和解释的有效辅助手段,而且是研究地球深部精细构造和地球深部探测的有效工具.射线理论和波动方程理论是地震波场数值模拟的理论基础.射线理论主要刻画地震波在介质中传播的走时场、地震射线等运动学属性;波动方程理论通过求解波动方程来描述地震波在介质中传播的弹性动力学响应(能量衰减、相位特征、偏振属性、以及全波形等).基于波动方程理论的波场数值模拟由于能够引入丰富的波场信息,使得人们对不同介质中地震波的传播过程有了较全面的了解.本文以二维层状均匀介质模型为例,通过射线追踪法和交错网格有限差分法模拟得到的波场快照图、单炮地震记录剖面、合成理论地震图的分析比较,不但对地震波在各向同性层状均匀介质中的传播规律和特点有了深刻的理解和认识,同时又可以相互验证两种不同方法的正确性和有效性.     

线性粘弹介质中地震波场数值模拟

本文将以往两种粘弹介质中地震波模拟方法的优点结合起来，以模型理论和积分本构方程为基础，从理论上分析了模型对地震波场的影响；采用交错网格有限差分法对粘弹介质中的地震波进行数值模拟.数值计算结果表明该方法不仅便于计算，同时也便于从力学的角度来分析地震波的传播.数值计算结果与理论分析一致，说明这种方法可以更为有效地模拟粘弹介质中地震波的传播.     

起伏层状介质中曲线网格有限差分法与射线法波场模拟对比研究

针对处理起伏地表(或含地下不规则波阻抗界面)条件下发展起来的地震波场数值模拟算法的模拟结果与解析解(大多数情形下无法得到)无法进行对比,且其有效性和正确性难以验证的情况,本文提出了一种可以相互验证波场数值模拟结果与射线追踪数值模拟结果的正确性和有效性的佐证方法,验证了参考射线追踪法.其中,波场数值模拟中采用曲线网格DRP/opt MacCormack有限差分法,射线追踪模拟则采用分区多步三角网格最短路径算法.通过系统对比上述两种方法得到的波场快照、单炮地震记录,以及合成理论地震图的结果显示,本方法相互作证了两种方法所得结果的正确性和有效性.双层和三层起伏层状模型的对比分析结果表明,这种方法不但可以加深理解地震波在复杂介质中的传播规律,同时射线法的引入为清晰识别和标定地震波场数值模拟中各种不同震相提供了一种便捷的途径.      

裂缝诱导双相HTI介质地震波场错格伪谱法模拟与波场特征分析

裂缝诱导的双相具有水平对称轴的横向各向同性(HTI)介质模型是由一组平行排列的垂直裂缝嵌入到统计各向同性的流体饱和多孔隙岩石中而组成的,它综合考虑了裂缝型储层岩石的各向异性和孔隙性.高精度的地震波场数值模拟技术是研究该介质中地震波传播规律的主要方法.本文结合错格伪谱法和时间分裂法,求解描述该介质中地震波传播的一阶速度-应力方程.模拟了单层和双层模型中的地震波场,并对其进行了特征分析.研究结果表明:错格伪谱法能有效消除标准网格伪谱法波场模拟结果中出现的数值伪影现象,与时间分裂法结合能够获得稳定的、高精度的模拟结果;裂缝诱导双相HTI介质中的地震波场兼具裂缝各向异性介质和双相介质中传播的地震波的波场特征.     

起伏地表弹性波传播的间断Galerkin有限元数值模拟方法

间断Galerkin有限元法（DG-FEM）作为一种有效的高阶有限元法受到了国内外学者的广泛关注.本文基于任意高阶间断Galerkin有限元法对弹性波方程进行空间离散,并将离散后所得的非齐次线性常微分方程系统齐次化,最后结合针对齐次问题的强稳定性保持龙格库塔（SSP Runge-Kutta）算法,将DG-FEM推广至时间任意高阶精度.另外,借鉴近最佳匹配层（NPML）的思想,基于复频移（CFS）拉伸坐标变换推导了一种新的PML吸收边界条件（简称为CFS-NPML）,该CFS-NPML能够与DG-FEM算法很好地结合,形成有效的起伏地表地震波传播数值模拟技术.数值试验结果表明,DG-FEM具有高阶精度,可以适应任意复杂起伏地表和复杂构造情况下的弹性波传播数值模拟.同时,CFS-NPML对包括面波等震相的人为边界反射都具有良好的吸收效果.     

Contribution to the knowledge of the magmatic evolution by the study of the variation of the coefficient of viscosity

The determination of the coefficient of viscosity of eruptive products gives useful elements to the knowledge of possible variations of composition and physical conditions of the magmas.     

Pictorial Series of the Manifestations of the Dynamics of the Earth

Studia Geophysica et Geodaetica -     

On the solution of the reverse problem of geodesics with the help of the chord

Резюме Дается вывод формул для вычислений длины хорды, длины и азимутов нормаляных сечений и длины геодезической линии эллипсоида. Применяются тригонометрические функции данных величин и постоянные принятого ргфгргнц-эллипсоида, что является целесообразным при использовании вычислителQjных машин, особенно автоматов. Рабочие формулы рекомендуются в форме (8–11).

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Dedicated to Professor František Fiala on His 85th Birthday

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Address: Veveři 95, Brno.     

Evolution of the Source of the Active Region of the Sun

Geomagnetism and Aeronomy - The magnetic evolution of the active region of the Sun at the level of the photosphere has been studied. Magnetic synoptic maps of the 2007 Kitt Peak Observatory were...     

On the gravimetric undulations of the geoid and the deflections of the vertical

Summary The author mentions the aims of the World-wide gravity project he established in the Ohio State University in Columbus, in 1950. He outlines the practical procedure of the gravimetric computations of the undulationsN and the vertical deflection components and and emphasizes that only by the global international cooperation and additional gravity observations at sea carried out during the last decade it has been possible to gather to Columbus the needed gravity material. Since there exist still large gravimetrically unsurveyed areas it is of vital significance to study what gravity anomalies are best to be used for these regions. The given figures concerning the accuracy of theN, and , estimated theoretically and obtained in practice, indicate that in the gravimetrically well surveyed parts of the world like in Europe and the United States we can get gravimetrically on basis of existing gravity material theN-values with accuracy of about 5–10 meters, and and with the accuracy of about 1. The geoid undulationsN are already computed in Columbus for more than 6000 points of the northern hemisphere. The sample maps show the interesting geoid of Europe and vicinity between the latitudes 60° and 30° and longitude 5° W and 30° E, drafted on basis of more than 1000N-values computed at the corners of 1°×1° squares. It is interesting to realize that the geoid undulations in all this area are positive, the extreme values being between 40 and 50 meters. The geophysical significance of the geoid maps of this kind is pointed out.     

Magnetic stratigraphy of the Ordovician in the lower reach of the Kotuy River: the age of the Bysy-Yuryakh stratum and the rate of geomagnetic reversals on the eve of the superchron

Until recently, the existing data prevented the geophysicists from accurately dating the Bysy-Yuryakh stratum, which outcrops in the middle reach of the Kotuy River, constraining the time of its formation to a wide interval from the end of the Late Cambrian to the beginning of the Silurian. The obtained paleomagnetic data unambiguously correlate the Bysy-Yuryakh stratum to the Nyaian regional stage and constrain its formation, at least a considerable part of it, by the Tremadocian. This result perfectly agrees with the data on the Bysy-Yuryakh conodonts studied in this work and yields a spectacular example of the successful application of paleomagnetic studies in solving important tasks of stratigraphy and, correspondingly, petroleum geology. Within the Bysy-Yuryakh stratum, we revealed a large normal-polarity interval corresponding to the long (>1 Ma) period when the geomagnetic reversals were absent. This result, in combination with the data for the Tremadocian and Middle–Upper Cambrian sequences of the other regions, indicates that (1) the rate of occurrence of the geomagnetic reversals on the eve of the Ordovician Moyero superchron of reversed polarity was at most one reversal per Ma; (2) the superchron does not switch on instantaneously but is preceded by a certain gradual change in the operation conditions of the dynamo mechanism which, inter alia, manifests itself by the reduction of the frequency of geomagnetic reversals with the approach of the superchron. This finding supports the views according to which a process preparing the establishment of the superchrons takes place at the core–mantle boundary.     

The effect of the pollution of the ground layer of the atmosphere on the albedo

Summary A simple model is proposed suitable for studying the effect of the ground layer of the atmosphere, polluted by aerosol, on the albedo. This model is founded on solving the equation of transfer of radiative energy. The numerical results are discussed, particular attention being paid to the analysis of errors due to neglecting the multiple reflection of solar radiation on the aerosol particles. A method which would also include the multiple reflection is proposed, and the conditions under which the presence of the aerosol is responsible for an increase or decrease of the solar radiation balance on the Earth's surface, are analysed.     

On the maintenance of the axisymmetric part of the flow in the atmosphere

Summary The maintenance of the axisymmetric component of the flow in the atmosphere is investigated by means of a steady-state, quasi-geostrophic formulation of the meteorological equations. It is shown that the meridional variations in the time-averaged axisymmetric variables can be expressed as the sum of three contributions, one being due to the eddy heat transport, another to the eddy momentum transport, and a third to the convective-radiative equilibrium temperature which enters the problem through the specification of a Newtonian form of diabatic heating. The contributions by the large scale eddies are evaluated through the use of observed values for the eddy heat and momentum transports.The contributions from each of the three forcing mechanisms to the temperature and zonal wind fields are invstigated individually and found to be of about equal importance. The sum of the three contributions are also presented for the temperature, the zonal wind, the stream function associated with the mean meridional circulation and the corresponding vertical motion. Although the results fail to reproduce the main observed features of the lower stratosphere, they are found to be in good agreement with observations in the middle latitude troposphere. At any pressure level, for example, the computed mean zonal wind has a jet-like profile and the axis of the jet is found to slope to the south with height, as observed in the atmosphere.Based in part on a thesis submitted by the first author as partial fulfillment of the requirements for the Ph.D. degree at the University of Michigan. — Publication No. 194 from the Department of Meteorology and Oceanography, The University of Michigan.     

On the determination of the non-linearity of the gravimeter scale

Summary The results of two different methods of the determination of the non-linearity of the gravimeter scale are compared; the economy is discussed as well.